# Age-Technology Interaction Tests

*Motivated by Crouzet, Ghosh, Gupta & Mezzanotti (2026), who show younger populations adopt technology faster at the micro level (India mobile payments). Tests whether the demographic effect on capital intensity and labor productivity is amplified in high-connectivity settings.*

## Test 1: Do Demographics Predict Technology Adoption?

If aging populations adopt technology more slowly (Crouzet et al.), Z₁ should negatively predict internet penetration, mobile subscriptions, and R&D spending.

| Model | Z₁ | se | p | Z₂ | p | N | Countries | R² |
|:--|--:|--:|--:|--:|--:|--:|--:|--:|
| Full: internet_users_pct | -114.7*** | 20.7 | 0.000 | 26.7 | 0.000 | 3941 | 164 | 0.279 |
| OECD: internet_users_pct | -237.4*** | 88.4 | 0.007 | 29.6 | 0.015 | 1005 | 37 | -0.050 |
| Non-OECD: internet_users_pct | -187.0*** | 19.5 | 0.000 | 41.0 | 0.000 | 2936 | 127 | 0.178 |
| Full: mobile_subs_per100 | 7.8 | 42.8 | 0.856 | 14.7 | 0.023 | 4218 | 164 | 0.180 |
| OECD: mobile_subs_per100 | -116.0 | 137.3 | 0.398 | 17.4 | 0.357 | 1014 | 37 | -0.293 |
| Non-OECD: mobile_subs_per100 | -51.3 | 47.5 | 0.281 | 27.9 | 0.000 | 3204 | 127 | 0.144 |
| Full: rd_gdp | 0.8 | 0.8 | 0.286 | -0.1 | 0.208 | 1874 | 132 | 0.345 |
| OECD: rd_gdp | -4.8** | 2.3 | 0.039 | 0.6 | 0.077 | 798 | 37 | 0.160 |
| Non-OECD: rd_gdp | 0.5 | 0.7 | 0.487 | -0.0 | 0.810 | 1076 | 95 | 0.183 |
| Full: log_patents | 1.8 | 2.6 | 0.472 | -0.0 | 0.912 | 2470 | 133 | 0.178 |
| OECD: log_patents | -2.3 | 3.5 | 0.511 | 0.5 | 0.266 | 973 | 37 | 0.100 |
| Non-OECD: log_patents | 1.3 | 3.5 | 0.710 | 0.1 | 0.905 | 1497 | 96 | -0.031 |

## Test 2: Z₁ × Technology Interaction on Capital Intensity and Productivity

Does high technology adoption amplify or dampen the demographic effect on capital intensity? If younger populations adopt technology faster AND technology substitutes for labor, then Z₁ × internet should be positive (aging + low tech = less automation).

| Outcome | Tech moderator | Z₁ | p | Z₁×Tech | se | p | N | R² |
|:--|:--|--:|--:|--:|--:|--:|--:|--:|
| capital_per_worker | internet_users_pct | 0.1** | 0.027 | 0.0*** | 0.0 | 0.000 | 3918 | 0.527 |
| capital_per_worker | mobile_subs_per100 | 0.1 | 0.157 | 0.0*** | 0.0 | 0.000 | 4196 | 0.482 |
| capital_per_worker | rd_gdp | 0.3*** | 0.002 | 0.0* | 0.0 | 0.058 | 1874 | 0.593 |
| capital_per_worker | log_patents | 0.2*** | 0.004 | 0.0*** | 0.0 | 0.001 | 2467 | 0.567 |
| log_labor_productivity | internet_users_pct | 1.9*** | 0.000 | 0.0*** | 0.0 | 0.000 | 3874 | 0.866 |
| log_labor_productivity | mobile_subs_per100 | 1.8*** | 0.000 | 0.0*** | 0.0 | 0.000 | 4142 | 0.846 |
| log_labor_productivity | rd_gdp | 2.0*** | 0.000 | 0.0 | 0.0 | 0.332 | 1862 | 0.925 |
| log_labor_productivity | log_patents | 2.0*** | 0.000 | 0.0 | 0.0 | 0.369 | 2428 | 0.867 |

## Test 3: Income-Conditioned Technology Interactions

Crouzet et al.'s India finding suggests the age-technology nexus may be strongest in developing countries where technology leapfrogging is possible. Test Z₁ × internet by income tercile.

| Tercile | Outcome | Z₁ | p | Z₁×Internet | p | N | Countries |
|:--|:--|--:|--:|--:|--:|--:|--:|
| Low income | capital_per_worker | 0.1* | 0.069 | 0.0*** | 0.000 | 1132 | 50 |
| Low income | log_labor_productivity | 2.0*** | 0.000 | 0.1*** | 0.000 | 1113 | 50 |
| Mid income | capital_per_worker | -0.1* | 0.069 | 0.0** | 0.039 | 1322 | 56 |
| Mid income | log_labor_productivity | 1.2*** | 0.005 | 0.0* | 0.060 | 1345 | 57 |
| High income | capital_per_worker | 0.1 | 0.535 | 0.0*** | 0.001 | 1416 | 55 |
| High income | log_labor_productivity | 0.4 | 0.254 | 0.0*** | 0.000 | 1416 | 55 |

## Test 4: Technology Adoption as Mediator

If demographics → technology → capital intensity, then controlling for internet/mobile should attenuate Z₁ on capital intensity.

| Model | Z₁ | se | p | Attenuation | N | R² |
|:--|--:|--:|--:|--:|--:|--:|
| Baseline (no tech) | 0.1* | 0.0 | 0.095 | — | 4517 | 0.473 |
| + internet_users | 0.1** | 0.0 | 0.013 | -58% | 3918 | 0.520 |
| + mobile_subs | 0.0 | 0.0 | 0.310 | 37% | 4196 | 0.476 |
| + R&D/GDP | 0.2*** | 0.1 | 0.002 | -233% | 1874 | 0.590 |
| + all tech controls | 0.3*** | 0.1 | 0.000 | -370% | 1851 | 0.608 |

**Same-sample diagnostic (critical):** The -370% figure is misleading. The restricted sample (N=1,851) has a much stronger baseline than the full sample:

| Model | Z₁ | p | N | Note |
|:--|--:|--:|--:|:--|
| Full sample baseline | 0.07 | 0.095 | 4,517 | Full |
| Restricted sample baseline | 0.27 | 0.001 | 1,851 | Same obs as +all tech |
| Restricted + all tech | 0.35 | 0.000 | 1,851 | Genuine amplification |
| Internet same-sample baseline | 0.07 | 0.172 | 3,918 | Same obs as +internet |
| + internet (same sample) | 0.12 | 0.013 | 3,918 | ~80% same-sample suppression |

**Corrected assessment:** Most of the apparent amplification (0.07→0.27) is **sample composition** — countries with tech data are richer. The genuine same-sample internet suppression is ~80% (0.07→0.12). Mobile shows zero suppression. R&D shows zero on its own sample (0.26→0.25). The suppression is real but modest.

## Test 5: Lag and First-Difference Robustness

| Model | Z₁ | p | Interaction | p | N | R² |
|:--|--:|--:|--:|--:|--:|--:|
| 5yr lag internet: capital_per_worker | 0.2*** | 0.006 | 0.0*** | 0.000 | 3363 | 0.572 |
| 5yr lag internet: log_labor_productivity | 1.9*** | 0.000 | 0.0** | 0.028 | 3326 | 0.896 |
| First-diff: ΔK/L ~ Z + Δinternet | -0.0** | 0.012 | — | — | 3743 | 0.092 |

## Test 6: Demographics → CA, Technology Channel

Crouzet et al. argue technology adoption affects trade competitiveness. If Z → technology → trade → CA, then controlling for internet should attenuate Z₁ on CA/GDP.

| Model | Z₁ | se | p | Attenuation | N | R² |
|:--|--:|--:|--:|--:|--:|--:|
| CA baseline | 3.0 | 12.2 | 0.805 | — | 4406 | 0.185 |
| CA + internet | -3.2 | 13.2 | 0.806 | 207% | 3851 | 0.202 |
| CA + R&D | 32.6** | 14.8 | 0.027 | -985% | 1861 | 0.369 |

## Synthesis

1. **Demographics → technology adoption:** 1/4 technology indicators show significant Z₁ effects in the full sample.

2. **Z₁ × technology interactions:** 5/8 interaction tests are significant.

3. **Suppression (corrected):** Same-sample internet suppression is ~80%. The raw -370% figure is a sample composition artifact.

### Connection to Crouzet et al. (2026)

Crouzet et al. show that younger populations adopt mobile payments faster in India, suggesting technology adoption as a channel through which demographics affect economic outcomes. Our tests examine whether this micro-level finding aggregates to the macro level: do countries with younger populations have higher technology adoption, and does technology moderate the demographic effect on capital accumulation? The results inform whether the automation paper's K/L deepening finding operates partly through a technology adoption channel.

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*Generated: March 8, 2026. Panel: automation_panel.csv + WDI tech indicators (237 countries, 1990-2024).*